Chapter XXXIV: Appendix: J

ON THE MEASUREMENT OF ALTITUDES BY THE BOILING-POINT THERMOMETER.

The use of the boiling-point thermometer for the determination of elevations in mountainous countries appearing to me to be much underrated, I have collected the observations which I was enabled to take, and compared their results with barometrical ones.

I had always three boiling-point thermometers in use, and for several months five; the instruments were constructed by Newman, Dollond, Troughton, and Simms, and Jones, and though all in one sense good instruments, differed much from one another, and from the truth. Mr. Welsh has had the kindness to compare the three best instruments with the standards at the Kew Observatory at various temperatures between 180 degrees and the boiling-point; from which comparison it appears, that an error of l.5 degrees may be found at some parts of the scale of instruments most confidently vouched for by admirable makers. Dollond's thermometer, which Dr. Thomson had used throughout his extensive west Tibetan journeys, deviated but little from the truth at all ordinary temperatures. All were so far good, that the errors, which were almost entirely attributable to carelessness in the adjustments, were constant, or increased at a constant ratio throughout all parts of the scale; so that the results of the different instruments have, after correction, proved strictly comparable.

The kettle used was a copper one, supplied by Newman, with free escape for the steam; it answered perfectly for all but very high elevations indeed, where, from the water boiling at very low temperatures, the metal of the kettle, and consequently of the thermometer, often got heated above the temperature of the boiling water.

I found that no confidence could be placed in observations taken at great elevations, by plunging the thermometer in open vessels of boiling water, however large or deep, the abstraction of heat from the surface being so rapid, that the water, though boiling below, and hence bubbling above, is not uniformly of the same temperature throughout.

In the Himalaya I invariably used distilled, or snow or rain-water; but often as I have tried common river-water for comparison, I never found that it made any difference in the temperature of the boiling-point. Even the mineral-spring water at Yeumtong, and the detritus-charged glacial streams, gave no difference, and I am hence satisfied that no objection can be urged against river waters of ordinary purity.

On several occasions I found anomalous rises and falls in the column of mercury, for which I could not account, except theoretically, by assuming breaks in the column, which I failed to detect on lifting the instrument out of the water; at other times, I observed that the column remained for several minutes stationary, below the true temperature of the boiling water, and then suddenly rose to it. These are no doubt instrumental defects, which I only mention as being sources of error against which the observer must be on the watch: they can only be guarded against by the use of two instruments.

With regard to the formula employed for deducing the altitude from a boiling-point observation, the same corrections are to a great extent necessary as with barometric observations: if no account is taken of the probable state of atmospheric pressure at the level of the sea at or near the place of observation, for the hour of the day and month of the year, or for the latitude, it is obvious that errors of 600 to 1000 feet may be accumulated. I have elsewhere stated that the pressure at Calcutta varies nearly one inch (1000 feet), between July and January; that the daily tide amounts to one-tenth of an inch (=100 feet); that the multiplier for temperature is too great in the hot season and too small in the cold; and I have experimentally proved that more accuracy is to be obtained in measuring heights in Sikkim, by assuming the observed Calcutta pressure and temperature to accord with that of the level of the sea in the latitude of Sikkim, than by employing a theoretical pressure and temperature for the lower station.

In the following observations, the tables I used were those printed by Lieutenant-Colonel Boileau for the East India Company's Magnetic Observatory at Simla, which are based upon Regnault's Table of the 'Elastic Force of Vapour.' The mean height of the barometrical column is assumed (from Bessel's formula) to be 29.924 at temp. 32 degrees, in lat. 45 degrees, which, differing only .002 from the barometric height corresponding to 212 degrees Fahrenheit, as determined experimentally by Regnault, gives 29.921 as the pressure corresponding to 212 degrees at the level of the sea.

The approximate height in feet corresponding to each degree of the boiling-point, is derived from Oltmann's tables. The multipliers for the mean temperature of the strata of atmosphere passed through, are computed for every degree Fahrenheit, by the formula for expansion usually employed, and given in Baily's Astronomical Tables and Biot's Astronomie Physique.

For practical purposes it may be assumed that the traveller, in countries where boiling-point observations are most desired, has never the advantage of a contemporaneous boiling-point observation at a lower station. The approximate difference in height is hence, in most cases, deduced from the assumption, that the boiling-point temperature at the level of the sea, at the place of observation, is 212 degrees, and that the corresponding temperature of the air at the level of the sea is hotter by one degree for every 330 feet of difference in elevation. As, however, the temperature of boiling water at the level of the sea varies at Calcutta between July and January almost from 210.7 degrees to 212.6 degrees, I always took the Calcutta barometer observation at the day and hour of my boiling-point observation, and corrected my approximate height by as many feet as correspond to the difference between the observed height of the barometer at Calcutta and 29.921; this correction was almost invariably (always normally) subtractive in the summer, often amounting to upwards of 400 feet: it was additive in winter, and towards the equinoxes it was very trifling.

For practical purposes I found it sufficient to assume the Calcutta temperature of the air at the day and hour of observation to be that of the level of the sea at the place of observation, and to take out the multiplier, from the mean of this and of the temperature at the upper station. As, however, 330 feet is a near approach to what I have shown (Appendix I.) to be the mean equivalent of 1 degree for all elevations between 6000 and 18,000 feet; and as the majority of my observations were taken between these elevations, it results that the mean of all the multipliers employed in Sikkim for forty-four observations amounts to 65.1 degrees Fahrenheit, using the Calcutta and upper station observations, and 65.3 degrees on the assumption of a fall of 1 degree for every 330 feet. To show, however, how great an error may accrue in individual cases from using the formula of 1 degree to 330, I may mention that on one occasion, being at an elevation of 12,000 feet, with a temperature of the air of 70 degrees, the error amounted to upwards of 220 feet, and as the same temperature may be recorded at much greater elevations, it follows that in such cases the formula should not be employed without modification.

A multitude of smaller errors, arising from anomalies in the distribution of temperature, will be apparent on consulting my observations on the temperature at various elevations in Sikkim; practically these are unavoidable. I have also calculated all my observations according to Professor J. Forbes's formula of 1 degree difference of temperature of boiling-water, being the equivalent of 550 feet at all elevations. (See Ed. Phil. Trans., vol xv. p. 405.) The formula is certainly not applicable to the Sikkim Himalaya; on the contrary, my observations show that the formula employed for Boileau's tables gives at all ordinary elevations so very close an approach to accuracy on the mean of many observations, that no material improvement in its construction is to be anticipated.

At elevations below 4000 feet, elevations calculated from the boiling-point are not to be depended on; and Dr. Thomson remarked the same in north-west India: above 17,000 feet also the observations are hazardous, except good shelter and a very steady fire is obtainable, owing to the heating of the metal above that of the water. At all other elevations a mean error of 100 feet is on the average what is to be expected in ordinary cases. For the elevation of great mountain masses, and continuously elevated areas, I conceive that the results are as good as barometrical ones; for the general purposes of botanical geography, the boiling-point thermometer supersedes the barometer in point of practical utility, for under every advantage, the transport of a glass tube full of mercury, nearly three feet long, and cased in metal, is a great drawback to the unrestrained motion of the traveller.

In the Khasia mountains I found, from the mean of twelve stations and twenty-three observations, the multiplier as derived from the mean of the temperature at the upper station and at Calcutta, to be 75.2 degrees, and as deduced from the formula to be 73.1 degrees. Here, however, the equivalent in feet for 1 degree temp. is in summer very high, being 1 degree=385 feet. (See Appendix I.) The mean of all the elevations worked by the boiling-point is upwards of 140 feet below those worked by the barometer.

The following observations are selected as having at the time been considered trustworthy, owing to the care with which they were taken, their repetition in several cases, and the presumed accuracy of the barometrical or trigonometrical elevation with which they are compared. A small correction for the humidity of the air might have been introduced with advantage, but as in most barometrical observations, the calculations proceed on the assumption that the column of air is in a mean state of saturation; as the climate of the upper station was always very moist, and as most of the observations were taken during the rains, this correction would be always additive, and would never exceed sixty feet.

It must be borne in mind that the comparative results given below afford by no means a fair idea of the accuracy to be obtained by the boiling-point. Some of the differences in elevation are probably due to the barometer. In other cases I may have read off the scale wrong, for however simple it seems to read off an instrument, those practically acquainted with their use know well how some errors almost become chronic, how with a certain familiar instrument the chance of error is very great at one particular part of the scale, and how confusing it is to read off through steam alternately from several instruments whose scales are of different dimensions, are differently divided, and differently lettered; such causes of error are constitutional in individual observers. Again, these observations are selected without any reference to other considerations but what I have stated above; the worst have been put in with the best. Had I been dependent on the boiling-point for determining my elevations, I should have observed it oftener, or at stated periods whenever in camp, worked the greater elevations from the intermediate ones, as well as from Calcutta, and resorted to every system of interpolation. Even the following observations would be amended considerably were I to have deduced the elevation by observations of the boiling-point at my camp, and added the height of my camp, either from the boiling-point observations there, or by barometer, but I thought it better to select the most independent method of observation, and to make the level of the sea at Calcutta the only datum for a lower station.

SERIES I.--_Sikkim Observations._

Elev. by Barom. or Temp. Elev. Place. Month. Trigonom. B.P. Air by B.P. Error (feet) (feet) (feet) ------------------------------------------------------------------------ Great Rungeet river Feb. B 818 210.7 56.3 904 + 86 Bhomsong Dec. 1,544 210.2 58.0 1,321 -223 Guard House, Gt Rungeet April 1,864 208.1 72.7 2,049 +185 Choongtam Aug. 5,268 202.6 65.0 5,175 - 93 Dengha Aug. 6,368 200.6 68.0 6,246 -122 Mr. Muller's (Dorjiling) Feb. Tr 6,925 199.4 41.3 7,122 +197 Dr. Campbell's (do.) April 6,932 200.1 59.5 6,745 -187 Mr. Hodgson's (do.) Feb. B 7,429 199.4 47.6 7,318 -111 Sinchul Jan. Tr 8,607 197.0 41.7 8,529 - 78 Lachoong Aug. B 8,712 196.4 54.6 8,777 + 65 Lamteng Aug. 8,884 196.3 77.0 8,937 + 53 Zemu Samdong July 8,976 196.1 58.6 8,916 - 60 Mainom Dec. Tr 10,702 193.4 38.0 10,516 -186 Junct. of Zemu & Thlonok July B 10,846 193.6 52.0 10,872 + 26 Tallum July 11,482 191.8 54.6 11,451 - 31 Yeumtong Sept. 11,919 191.3 52.2 11,887 - 32 Zemu river June 12,070 190.4 48.5 12,139 + 69 Tungu July & 12,751 189.7 43.4 12,696 - 55 Oct. Jongri Jan. 13,194 188.8 26.0 13,151 - 43 Zemu river June 13,281 188.5 47.0 13,360 + 79 Lachee-pia Aug. 15,262 186.0 42.8 14,912 -350 Momay Sept. 15,362 186.1 48.6 14,960 -402 Palung Oct. 15,620 185.4 45.8 15,437 -183 Kongra Lama July 15,694 184.1 41.5 16,041 +347 Snow-bed above Yeumtong Sept. 15,985 184.6 44.5 15,816 -169 Tunkra pass Aug. 16,083 164.1 39.0 16,137 + 54 Yeumtso Oct. 16,808 183.1 15.0 16,279 -529 Donkia Sept. 16,978 182.4 41.0 17,049 + 71 Mountain above Momay Sept. 17,394 181.9 47.8 17,470 + 76 Sebolah pass Sept. 17,585 181.9 46.5 17,517 - 68 Kinchinjhow Sept. 17,624 181.0 47.5 18,026 +402 Donkia Mountain Sept. 18,510 180.6 37.1 18,143 -367 Ditto Sept. 18,307 179.9 38.8 18,597 +290 Bhomtso Oct. 18,450 181.2 52.0 18,305 -145 Donkia pass Sept. 18,466 181.2 45.5 17,866 -600 ------------------------------------------------------------------------ Mean - 58

SERIES II.--_Khasia Mountains._

Elev. Elev. Place Month Bar. B.P. Tm. Air by B.P. Diff. (feet) (feet) (feet) ---------------------------------------------------------------------- Churra June 4,069 204.4 70.3 4,036 - 33 Amwee Sept. 4,105 205.1 67.7 4,041 - 64 Nurtiung Oct. 4,178 205.0 70.0 4,071 -107 Nunklow July 4,688 203.9 69.8 4,333 -355 Kala-panee June, July, 5,302 202.2 65.8 5,202 -100 Sept., Oct. Myrung July 5,647 201.9 69.4 5,559 - 88 Syong July 5,725 201.8 70.8 5,632 - 93 Moflong July, Aug., 6,062 201.4 64.8 5,973 - 89 Oct., Nov. Chillong Nov. 6,662 201.2 62.8 6,308 -354 ---------------------------------------------------------------------- Mean 5,160 5,016 -143